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Math Help - differential form and wedge product

  1. #1
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    differential form and wedge product

    Hello,

    i have a little question: If f is a differential form. Is then f \wedge f=0?

    I think so, but i'm not sure, because i never work with forms before. Here is my proof:

    let f:M->\Lambda(M) be a k-form and T^k the Alternator. then we get
    (f \wedge f)(P)=f(p)\wedge f(p)=\frac{(2k)!}{k!k!}*T^{2k}(f(p)\otimes f(p))=0
    because T^{2k}(f(p)\otimes f(p))=0

    Is this correct?

    Regards
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  2. #2
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    \sigma = dx \wedge dy + dz \wedge dw
    \sigma \wedge \sigma = (dx \wedge dy + dz \wedge dw)\wedge(dx \wedge dy + dz \wedge dw)
    =dx \wedge dy \wedge dz \wedge dw + dz \wedge dw \wedge dx \wedge dy
    =2 dx \wedge dy \wedge dz \wedge dw
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  3. #3
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    Hello,

    thank you very much. Can you tell me why this is a differential form?
    Can i also think of f=e_1 \wedge e_2 + e_3 \wedge e_4??


    Regards
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  4. #4
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    What is your definition of a differential form?
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  5. #5
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    Our definition is:

    A differential form is a smooth section of the natural projection.

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